W. R. Dedekind. The first presents Dedekind's theory of the irrational number-the Dedekind cut idea-perhaps the most famous of several such theories created in the 19th century to give a precise meaning to irrational numbers, which had been used on an intuitive basis since Greek times. This paper provided a purely arithmetic and perfectly rigorous foundation for the irrational numbers and thereby a rigorous meaning of continuity in analysis.The second essay is an attempt to give a logical basis for transfinite numbers and properties of the natural numbers. It examines the notion of natural numbers, the distinction between finite and transfinite (infinite) whole numbers, and the logical validity of the type of proof called mathematical or complete induction.The contents of these essays belong to the foundations of mathematics and will be welcomed by those who are prepared to look into the somewhat subtle meanings of the elements of our number system. As a major work of an important mathematician, the book deserves a place in the personal library of every practicing mathematician and every teacher and historian of mathematics. Authorized translations by "Vooster " V. Beman.

    His fame was such that many Greek medical writings became attributed to him. What they have in common is not dogma but, rather, constructive debate between one another. They also share a concern with meticulous observation and an insistence on physical, not supernatural, causation of illness. The writers were the pioneers of rational medicine; their ideas, dominant for centuries, still reveal to us the ideal of ethical practice, as well as the origins not just of Western medicine but of scientific method.This excellent selection of Hippocratic treatises shows the range of writing and thought. Some are technical works on embryology, surgery or anatomy; others are addressed to a lay audience; all are informed with the spirit of inquiry. G.E.R. Lloyd's authoritative introduction puts them into their contemporary context and assesses their later influence.

    In the three years that followed, Luther clarified and defended his position in numerous writings. Chief among these are the three treatises written in 1520. In these writings Luther tried to frame his ideas in terms that would be comprehensible not only to the clergy but to people from a wide range of backgrounds. [i]To the Christian Nobility of the German Nation[/i] is an attack on the corruption of the church and the abuses of its authority, bringing to light many of the underlying reasons for the Reformation. The second treatise, [i]The Babylonian Captivity of the Church[/i], contains Luther's sharp criticism of the sacramental system of the Catholic church. [i[The Freedom of a Christian[/i] gives a concise presentation of Luther's position on the doctrine of justification by faith. The translations of these treatises are all taken from the American edition of Luther's Works. This new edition of [i]Three Treatises[/i] will continue to be a popular resource for individual study, church school classes, and college and seminary courses.

    SIR: THESE thoughts concerning education, which now come abroad into the world, do of right belong to you, being written several years since for your sake, and are no other than what you have already by you in my letters. I have so little vary'd any thing, but only the order of what was sent you at different times, and on several occasions, that the reader will easily find, in the familiarity and fashion of the stile, that they were rather the private conversation of two friends, than a discourse design'd for publick view.

    

    For the alternate cover edition by Simon & Schuster, see hereClear and concise explanations of the development of theories explaining physical phenomena.

    Routledge is an imprint of Taylor & Francis, an informa company.

    Originally published in journals between 1884 and 1906, these 12 essays were selected by William James to illustrate the doctrine he called "radical empiricism" — a concept that made him the center of a new philosophic approach.Proclaiming experience to be the ultimate reality, James explores the applications of experience to the problem of relations, the role of feeling in experience, and the nature of truth. He argues in favor of a pluralistic universe, denying that experience can be defined in terms of an absolute force determining the relationships between things and events. Relationships, regardless of whether they hold things together or apart, are as real as the things themselves — their functions are real, and there are no hidden factors responsible for life's harmonies and dissonances.Seminal essays in this collection include "Does Consciousness Exist?: "The Essence of Humanism," and "Absolutism and Empiricism." In addition, this edition features a new translation of "On the Notion of Consciousness" — the first English rendering of the essay, which was written in French. Indispensable to an understanding of the great philosopher's other works, this systematic and compact treatment functions equally well in and out of the classroom.

    The reader may sense that Mill is being pulled in opposing directions: steadfastly committed to majority rule with minority rights while at the same time being just enough of an aristocrat to believe that the masses need examplars to emulate.On Representative Government is one of the most compelling political essays of the 19th century.

    St. Thomas Aquinas has much to teach us--most especially how to confront the classic questions that are still with us after centuries of thought.

    The central concept of his philosophy is found in a careful discrimination between the awareness of objects independent of our perception and the awareness of essences attributed to objects by our mind, or between what Santayana calls the realm of existents and the realm of subsistents. Since we can never be certain that these attributes actually inhere in a substratum of existents, skepticism is established as a form of belief, but animal faith is shown to be a necessary quality of the human mind. Without this faith there could be no rational approach to the necessary problem of understanding and surviving in this world.Santayana derives this practical philosophy from a wide and fascinating variety of sources. He considers critically the positions of such philosophers as Descartes, Euclid, Hume, Kant, Parmenides, Plato, Pythagoras, Schopenhauer, and the Buddhist school as well as the assumptions made by the ordinary man in everyday situations. Such matters as the nature of belief, the rejection of classical idealism, the nature of intuition and memory, symbols and myth, mathematical reality, literary psychology, the discovery of essence, sublimation of animal faith, the implied being of truth, and many others are given detailed analyses in individual chapters.

    It also includes ten essays that were withdrawn or left unpublished by Hume for various reasons.Eugene F. Miller was Professor of Political Science at the University of Georgia from 1967 until his retirement in 2003.Please note: This title is available as an ebook for purchase on Amazon, Barnes and Noble, and iTunes.

    Now, in the first translation into English since 1930, Aristotle's thought is presented accurately, with a lucid introduction and extensive notes to explain the general structure of each section of the book, and shed light on particular problems. It simplifies and expands the style of the original, making for easier reading and better comprehension.

    [captures] the relentless urgency of Lucretius' didacticism, his passionate conviction and proselytizing fervour.' --The Classical Review

    Many of the translations were done by Strachey himself; the rest were prepared under his supervision. The result was to place the Standard Edition in a position of unquestioned supremacy over all other existing versions. Newly designed in a uniform format, each new paperback in the Standard Edition opens with a biographical essay on Freud's life and work —along with a note on the individual volume—by Peter Gay, Sterling Professor of History at Yale.